{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6A32UE6YWTUQ62CX7Y7X3W7SRZ","short_pith_number":"pith:6A32UE6Y","canonical_record":{"source":{"id":"1503.06067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T13:41:55Z","cross_cats_sorted":[],"title_canon_sha256":"0efc7b3648e561d340c79208a2fccd7ded9c34c907a33a81a51b95aeea378a85","abstract_canon_sha256":"599520aa229fd19ccfb409bf742d920ffb1069943ae8e4e2b115cd5f64a66811"},"schema_version":"1.0"},"canonical_sha256":"f037aa13d8b4e90f6857fe3f7ddbf28e5123ba09c862f365881d37b444a5673b","source":{"kind":"arxiv","id":"1503.06067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06067","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06067v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06067","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"6A32UE6YWTUQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6A32UE6YWTUQ62CX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6A32UE6Y","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6A32UE6YWTUQ62CX7Y7X3W7SRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T13:41:55Z","cross_cats_sorted":[],"title_canon_sha256":"0efc7b3648e561d340c79208a2fccd7ded9c34c907a33a81a51b95aeea378a85","abstract_canon_sha256":"599520aa229fd19ccfb409bf742d920ffb1069943ae8e4e2b115cd5f64a66811"},"schema_version":"1.0"},"canonical_sha256":"f037aa13d8b4e90f6857fe3f7ddbf28e5123ba09c862f365881d37b444a5673b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:53.162946Z","signature_b64":"HeP6RV9X98QAyNGVvyOX2M24kfAXnTsCHiDIegGs6WTVwnMi806GEWfG5cG5jQUg6ZF7RzYzxwBohbIsRd3IDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f037aa13d8b4e90f6857fe3f7ddbf28e5123ba09c862f365881d37b444a5673b","last_reissued_at":"2026-05-18T01:31:53.162446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:53.162446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06067","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3aP43dTKB2g8OMPU0HaFKyuOAjkRKOmgyXquytd6IBrpSqfwEE+SRgeitFrIHqgBS2QwH3Ji6RMgEONWCpEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:45:42.192481Z"},"content_sha256":"5d0a63db146f561d4e332ea826a70e3c2afd726b23135f28c31a3c5365dd454f","schema_version":"1.0","event_id":"sha256:5d0a63db146f561d4e332ea826a70e3c2afd726b23135f28c31a3c5365dd454f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6A32UE6YWTUQ62CX7Y7X3W7SRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-theory for the tame C*-algebra of a separated graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Pere Ara, Ruy Exel","submitted_at":"2015-03-20T13:41:55Z","abstract_excerpt":"A {\\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$ and a set $C=\\bigsqcup_{v\\in E^0}C_v$, where each $C_v$ is a partition of the set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$, such that all the sets $X\\in C$ are finite, the K-theory of the graph C*-algebra $C^*(E,C)$ is known to be determined by the kernel and the cokernel of a certain map, denoted by $1_C- A_{(E,C)}$, from $\\mathbb Z^{(C)}$ to $\\mathbb Z^{(E^0)}$. In this paper, we compute the K-theory of the {\\it tame} graph C*-algebra $\\mathcal O(E,C)$ associated to $(E,C)$, which has b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06067","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJwxKuXzEYJsMffYvorUe2K6eywEcaCE/H4/L2xNPu7jSmgJQoWxcMhm4fiib+EoLrZfwrc7VVVd2T/uNq66Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:45:42.192836Z"},"content_sha256":"0d7f5cb0a52b476ba0650cc217b9a13730c69d4d07e286f805a96ebba2341256","schema_version":"1.0","event_id":"sha256:0d7f5cb0a52b476ba0650cc217b9a13730c69d4d07e286f805a96ebba2341256"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/bundle.json","state_url":"https://pith.science/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T07:45:42Z","links":{"resolver":"https://pith.science/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ","bundle":"https://pith.science/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/bundle.json","state":"https://pith.science/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6A32UE6YWTUQ62CX7Y7X3W7SRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6A32UE6YWTUQ62CX7Y7X3W7SRZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"599520aa229fd19ccfb409bf742d920ffb1069943ae8e4e2b115cd5f64a66811","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T13:41:55Z","title_canon_sha256":"0efc7b3648e561d340c79208a2fccd7ded9c34c907a33a81a51b95aeea378a85"},"schema_version":"1.0","source":{"id":"1503.06067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06067","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06067v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06067","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"6A32UE6YWTUQ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6A32UE6YWTUQ62CX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6A32UE6Y","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:0d7f5cb0a52b476ba0650cc217b9a13730c69d4d07e286f805a96ebba2341256","target":"graph","created_at":"2026-05-18T01:31:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A {\\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$ and a set $C=\\bigsqcup_{v\\in E^0}C_v$, where each $C_v$ is a partition of the set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$, such that all the sets $X\\in C$ are finite, the K-theory of the graph C*-algebra $C^*(E,C)$ is known to be determined by the kernel and the cokernel of a certain map, denoted by $1_C- A_{(E,C)}$, from $\\mathbb Z^{(C)}$ to $\\mathbb Z^{(E^0)}$. In this paper, we compute the K-theory of the {\\it tame} graph C*-algebra $\\mathcal O(E,C)$ associated to $(E,C)$, which has b","authors_text":"Pere Ara, Ruy Exel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T13:41:55Z","title":"K-theory for the tame C*-algebra of a separated graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06067","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5d0a63db146f561d4e332ea826a70e3c2afd726b23135f28c31a3c5365dd454f","target":"record","created_at":"2026-05-18T01:31:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"599520aa229fd19ccfb409bf742d920ffb1069943ae8e4e2b115cd5f64a66811","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-03-20T13:41:55Z","title_canon_sha256":"0efc7b3648e561d340c79208a2fccd7ded9c34c907a33a81a51b95aeea378a85"},"schema_version":"1.0","source":{"id":"1503.06067","kind":"arxiv","version":2}},"canonical_sha256":"f037aa13d8b4e90f6857fe3f7ddbf28e5123ba09c862f365881d37b444a5673b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f037aa13d8b4e90f6857fe3f7ddbf28e5123ba09c862f365881d37b444a5673b","first_computed_at":"2026-05-18T01:31:53.162446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:53.162446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HeP6RV9X98QAyNGVvyOX2M24kfAXnTsCHiDIegGs6WTVwnMi806GEWfG5cG5jQUg6ZF7RzYzxwBohbIsRd3IDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:53.162946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d0a63db146f561d4e332ea826a70e3c2afd726b23135f28c31a3c5365dd454f","sha256:0d7f5cb0a52b476ba0650cc217b9a13730c69d4d07e286f805a96ebba2341256"],"state_sha256":"fc10736395a617a6554a46ec45860f4bbfb0e80852570f5c7e607e85f9838c0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZK30bKAtrcphDJU/htYOMnlq+ZWPQ1WcrW6fwVYI2VqE5xPtT0HtRrphqABX2h2QODSskMxYwaL2sm3YRZrJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:45:42.194919Z","bundle_sha256":"8ca686d5e5631d229c13f44b21bd9930244d4a5ddcb041f070481800f2463639"}}